Simplify:

​$$(1 - sec^2\theta)(1 - sin\theta)(1 + sin\theta)(1 + cot^2\theta)$$

Correct option is B

Given: ​

​$$(1 - \sec^2\theta)(1 - \sin\theta)(1 + \sin\theta)(1 + \cot^2\theta)$$ 

Formula Used: ​

​$$\sec^2\theta = 1 + \tan^2\theta \\ \ \\1 + \cot^2\theta = \cosec^2\theta\\ \ \\(1 - \sin\theta)(1 + \sin\theta) = 1 - \sin^2\theta = \cos^2\theta \\ \ \\\tan\theta = \frac{\sin\theta}{\cos\theta}$$

Solution: 

$$(1 - \sec^2\theta)(1 - \sin\theta)(1 + \sin\theta)(1 + \cot^2\theta) \\\ \ \\ = (1 - \sec^2\theta)(1 - \sin^2\theta)(1 + \cot^2\theta)\\ \ \\ = (- \tan^2\theta)(\cos^2\theta)(\sec^2\theta)\\ \ \\\ = -\left(\frac{\sin^2\theta}{\cos^2\theta}\right)(\cos^2\theta)\left(\frac{1}{\sin^2\theta}\right) \\ \ \\ = -1$$​​